Fig. 4.

The scheme of the proof of Theorem 1. (A) an initial protocol evaluating function f with bias $1/6$, using Q qubits; (B) memoryless protocol, with the same bias, using $Q^2$ qubits; (C) protocol $\overline{P}$ using quantum correlations and $Q^2$ qubits, with bias still about $1/6$; (D) protocol $\overline{P}$ gives small bias for any classical correlation $R_c$ if $Q^2$ is sufficiently smaller than $C\left(f,2/3\right)$.